The OED has this to say about the matter, under the entry tinker, n. :

 "The low repute in which these, esp. the itinerant sort, were held in former times is shown by the expressions to swear like a tinker, a tinker's curse or damn, as drunk or as quarrelsome as a tinker, etc., and the use of ‘tinker’ as synonymous with ‘vagrant’, ‘gipsy’(sic) (see b)."

When we turn to b, we find:

 b. In Scotland and north of Ireland, the ordinary name for a gipsy: see TINKLER. Also, applied to itinerant beggars, traders, and performers generally; a vagabond, tramp, or reputed thief (obs.).   

The chief ostensible business of travelling gipsies in Scotland used to be the sale or mending of pots, pans, kettles, and metal-ware generally; hence tinkers, or rather tinklers, was their ordinary designation.

So it would seem that as Gypsies (and who likes a Gypsy) were disliked by nearly everyone, and apparently did much metalwork, their reputation was therefore applied to the occupation itself - hence the phrase. The "dam" bit is quite clearly nonsense. We are then further presented with a fairly interesting history of the phrase:

{1824 MACTAGGART Sir Balderdash v. in Gallovid. Encycl. s.v. Balderdash, A tinkler's curse she did na care What she did think or say.} 1839 THOREAU Jrnl. 25 Apr. in Writings (1906) VII. 78 'Tis true they are not worth a ‘tinker's damn’. 1865. {1877 KNIGHT Dict. Mech., (!)Tinker's-dam, a wall of dough raised around a place which a plumber desires to flood with a coat of solder. The material can be but once used; being consequently thrown away as worthless, it has passed into a proverb, usually involving the wrong spelling of the otherwise innocent word ‘dam’.}(!) 1884 St. James' Gaz.24 Apr. 12/1, I don't care two tinkers' straws if you do. 1891 KIPLING Light that Failed vii. 137 The real world doesn't care a tinker's doesn't care a bit. a1894 STEVENSON St. Ives xxv, I care not a Tinker's Damn for his ascension. 1907 Westm. Gaz. 28 Oct. 2/3 ‘A tinker's curse’, as used in the two new plays ‘Irene Wycherley’ and ‘The Barrier’. Ibid., (!)The suggestion that the phrase really refers to a ‘tinker's dam’..does credit to the speculative person who earliest associated it with the familiar old saying. (!). 1973 Jewish Chron. 2 Feb. 19/3 It doesn't matter a tinker's cuss whether you amend the constitution to call the chairman president. 1983 J. SYMONS Name of Annabel Lee II. viii. 139, I don't give a tinker's, if you'll forgive the old fashioned way of putting it, who killed Ira Wolfdal.

So, again, we see discussion of the "dam" theory, but the evidence to the contrary seems rather strong. Incidentally, while dannye's "Tin worker" theory seems to me quite plausible, the OED mentions the "metal-banging" otomonopoetic (sp?) theory, though it is not particularly confident in it.

Yeah, I know - it was more a less a cut 'n paste writeup. But I figure the fact that most people don't have access to the OED, plus my commentary, made it worth noding.